Should central banks be concerned with inequality? Traditionally, that is the domain of elected politicians. In fact, the crisis has seen a further blurring of the responsibilities of central bankers. Since the 1970s, monetary policy had been seen a highly technical area with a single instrument (the interest rate) and a single goal (controlling inflation). So it was natural to hand it over to officials.
The crisis has forced central bankers to expand their toolkit, and to make a much wider range of decisions – some of which have distributional effects. (So did interest rate hikes, but this used to be quietly ignored.)
Many Renaissance Italian city-states had a form of democracy. This democracy declined when the states began to hire experts as “city managers” - signori or capitani del popolo. Often these managers were from outside the city itself, rather as central bankers like Mark Carney are hired on a global market. As outsiders they could get things done in a way the squabbling democratic parties could not. But their rise hollowed out democratic power. Eventually, democracy became the “dignified”, not the “efficient” part of government.